On the saturation amplitude of the f-mode instability

TL;DR

This paper studies the nonlinear damping of neutron star oscillations, especially f modes, and estimates the gravitational wave signals they produce, providing upper limits on mode amplitudes and detectability with advanced interferometers.

Contribution

It introduces a nonlinear hydrodynamics simulation approach to determine saturation amplitudes of CFS-unstable f modes in neutron stars, considering various effects like rotation and EOS.

Findings

Nonlinear damping mainly due to shock formation and wave breaking.

Upper limits on f-mode saturation amplitudes derived from damping effects.

Gravitational waves from these modes could be detectable above 10 Mpc with advanced LIGO/VIRGO.

Abstract

We investigate strong nonlinear damping effects which occur during high amplitude oscillations of neutron stars, and the gravitational waves they produce. For this, we use a general relativistic nonlinear hydrodynamics code in conjunction with a fixed spacetime (Cowling approximation) and a polytropic equation of state (EOS). Gravitational waves are estimated using the quadrupole formula. Our main interest are l=m=2 f modes subject to the CFS (Chandrasekhar, Friedman, Schutz) instability, but we also investigate axisymmetric and quasiradial modes. We study various models to determine the influence of rotation rate and EOS. We find that axisymmetric oscillations at high amplitudes are predominantly damped by shock formation, while the nonaxisymmetric f modes are mainly damped by wave breaking and, for rapidly rotating models, coupling to nonaxisymmetric inertial modes. From the observed nonlinear damping, we derive upper limits for the saturation amplitude of CFS-unstable f modes. Finally, we estimate that the corresponding gravitational waves for an oscillation amplitude at the upper limit should be detectable with the advanced LIGO and VIRGO interferometers at distances above 10 MPc. This strongly depends on the stellar model, in particular on the mode frequency.